Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain (Communications in Mathematical Research, 2021)
A new Rogosinski-type kernel function is constructed using kernel function of partialsums $S_n(f;t)$ of generalized Fourier series on a parallel hexagon domain $Ω$ associating with three-direction partition. We prove that an operator $W_n(f;t)$ with the new kernel function convergesuniformly to any continuous function $f(t) ∈ C_∗(Ω)$ (the space of all continuous functions withperiod $Ω$) on $Ω$. Moreover, the convergence order of the operator is presented for the smoothapproached function.
Keywords: three-direction coordinate; kernel function; generalized Fourier series; uniform convergence.